COVID-19 transmission inside a small passenger vessel: Risks and mitigation

The global shipping industry has been severely influenced by the COVID-19 pandemic; in particular, a significant amount of passenger transportation has been suspended due to the concern of COVID-19 outbreak, as such voyages confine a dense crowd in a compact space. In order to accelerate the recovery of the maritime business and minimise passengers' risk of being infected, this work has developed a computational model to study the airborne transmission of COVID-19 viruses in the superstructure of a full-scale passenger vessel. Considering the vessel advancing in open water, simulations were conducted to study the particulate flow due to an infected person coughing and speaking, with the forward door open and closed. The results suggest that keeping the forward door closed will help prevent the external wind flow spreading the virus. When the forward door is closed, virus particles' coverage is shown to be limited to a radius of half a metre, less than a seat's width. Thus, an alternate seat arrangement is suggested. Furthermore, investigations were conducted on the influence of wall-mounted Air Conditioner (AC) on the virus transmission, and it was found that controlling the AC outlet direction at less than 15° downward can effectively limit the virus spread. Meanwhile, it was demonstrated that an AC's backflow tends to gather virus particles in a nearby area, thus sitting farther from an opening AC may reduce the risk of being infected. Overall, this work is expected to inform hygienic guidelines for operators to counter COVID-19 and potentially similar viruses in the future.


Introduction
The maritime industry has been severely affected by the COVID-19 pandemic. Ships are currently operating with reduced capacity or restricted from leaving port. In particular, the operation of passenger vessels has been reduced by up to 42.77% (Millefiori et al., 2021). Crew and passengers can be exposed to a serious risk of contagion, since the compact and crowded space of ships implies a high likelihood of COVID-19 outbreak. In this context, there is an urgent need to research the best technical solutions to ensure COVID-19 safety for ships (Thomas et al., 2021).
COVID-19 infection has been found to be primarily induced by inhalation (Jin et al., 2020). The virus can be transmitted via air, existing in a form of aerosols and droplets injected by humans coughing, speaking, breathing, singing and sneezing (Vuorinen et al., 2020). Coughing and speaking are the most likely scenarios, as coughing is one of the primary COVID-19 symptoms whilst speaking is almost inevitable in daily contacts and can actually output a significant amount of the virus (Chao et al., 2009). The transmission mechanism of the COVID-19 virus may be referred to in previous work that studied flu, as it has a similar mechanism to SARS (Gao and Niu, 2007).
To investigate the airborne transmission of COVID-19 virus, Computational Fluid Dynamics (CFD) has the capability to understand the virus's movement and coverage, which is essential for developing effective mitigation strategies for infection control. To date, computational studies of COVID-19 transmission have been conducted for certain high-risk areas. For example, Zhang et al. (2021a) performed a CFD analysis for virus transmission inside a bus. A simple air-spray experiment was also conducted to validate the CFD model (Zhang et al., 2021b). They compared the validated CFD results with the prediction from an analytical approach that was previously widely used. The comparison indicates that the analytical approach produces significant inaccuracies due to a lack of consideration of complex velocity and particle concentration fields. Thus they suggest that CFD should be used in future studies. Abuhegazy et al. (2020) and Talaat et al. (2021) used CFD to investigate the virus transmission in, respectively, a classroom and a passenger aeroplane; both papers suggest placing lateral shields/barriers between people sitting side-by-side, with simulations used to demonstrate their effectiveness. Guo et al. (2021) used CFD to study the virus transmission in hospital rooms. As the central AC system in hospitals may cause extensive spreading of the virus, they suggested placing portable air purifiers for mitigation and used simulations to identify the ideal locations for air purifiers. Welch et al. (2022) used CFD to demonstrate the effectiveness of using ultraviolet lights to limit the virus' airborne transmission.
Based on the above review, CFD has become a standard approach to studying COVID-19's airborne transmission in various scenarios. However, relevant research has not been seen for scenarios on board ships. During ship operations, natural winds, ACs and ventilation systems can induce airborne transmission of virus particles inside a vessel. The airflow environment on ships is unique due to its forward motion and the location of a doorway facing forward at the front of the passenger area which can be open. This open door may allow a significant wind flow in the passenger area when the ship is moving. In addition, relatively small ships usually use wall-mounted ACs instead of a central AC system. The airflow direction of the wall-mounted ACs can be adjusted, and the influence on COVID-19 transmission should be studied.
In this context, the present work develops a CFD-based model to analyse the potential transmission of the COVID-19 virus inside a ship. The paper starts by introducing the theories and practicalities of the model, followed by validating the model against experimental measurements of velocity field and particle diffusion inside an idealised room. Subsequently, the room geometry was replaced by the superstructure of a small passenger ship. Analyses were presented on the virus distribution in different scenarios, concerning a passenger coughing or speaking when the vessel's forward door is open or closed, and investigating the influence of AC winds on the virus spread. The obtained results were used to discuss measures that may minimise the spread and contagion risk of COVID-19 virus.

Computational approach
CFD is used to model airflow whilst the transmission of virus particles is tracked by a Lagrangian approach. The simulations were    performed using the commercial software STAR-CCM+.

Governing equations
In this work, Lagrangian particles are applied to model the COVID-19 virus aerosols/droplets, by which the particle movement is subjected to its gravity (G) and a drag force from its surrounding airflow (F d ): where m denotes the particle's mass, V P is the particle's velocity, G = mg and g is set at 9.81 m/s 2 . The fluid drag force is calculated through the Schiller-Naumann Correlation (Liu et al., 1993): where ρ P is the particle density, A P is the particle project area and V s is the relative velocity between the particle and the air. C d is an empirical coefficient calculated based on the particle's Reynolds number (Re P ), which is defined as follows.
The surrounding fluid flow is solved by the standard Reynolds-Averaged Navier-Stokes (RANS) equations: where v is the time-averaged velocity, v ′ is the velocity fluctuation, ρ is the fluid density (ρ air = 1 kg/m 3 ), p denotes the time-averaged pressure, τ = μ[∇v+ (∇v) T ] is the viscous stress term, μ is the dynamic viscosity (μ air = 1.48 × 10 − 5 N s/m 2 ). Since the RANS equations have considered the turbulent fluid, the Shear Stress Transport (SST) k − ω model was adopted to close the equations (Menter, 1993;Pena and Huang, 2021).
In particular, a sufficiently-small particle in turbulent flow reveals a randomly-varying velocity field, which induces the microscopic particles to perform constant stochastic motions thus diffusing. This behaviour is modelled by including the effect of instantaneous velocity fluctuations on the particle (Gosman and Loannides, 1983): To be more specific, the applied fluid velocity in calculations is v, which is different from a usual RANS approach for macroscopic problems where v is directly used to simplify the calculation, e.g. (Huang et al., 2020).

Validation
Based on the above governing equations, a validation study was conducted to reproduce the experiment of Chen et al. (2006). The experiment used artificial particles to mimic a flu virus, which has very similar particle dimensions, airborne transmission mechanism, and infection mechanism to COVID-19 virus. The experiment was conducted in a cubic chamber, with a size of 0.8 m × 0.4 m × 0.4 m, as shown in Fig. 1. The chamber has an air inlet near the left top side and an outlet near the right bottom side. The inlet and outlet sections are of the same size, 0.04 m × 0.04 m. The centers of them are located at x = 0, y = 0.2 m, z = 0.36 m and x = 0.8 m, y = 0.2 m, z = 0.04 m. Particles were injected from the inlet with airflow and diffused in the entire room. The velocity profile and particle distribution were measured across the centre plane of the chamber (the centre plane is marked in Fig. 1).
To reproduce the experiment, a computational domain of the same size, inlet and outlet was established, as shown in Fig. 2(a). The inlet was set as "fixed-velocity inlet" with a constant airflow velocity of (0.225, 0, 0) m/s, and the outlet was set as "fixed-pressure outlet" with a reference pressure of 0 Pa. This value is insignificant since the CFD calculation is based on relative pressure. Other boundaries are "non-slip walls". Spherical Particles of a diameter of 1 × 10 − 5 m and a density of 1.4 × 10 − 3 kg/m 3 were injected with the inlet flow, at a rate of 1000 particles per second. The particle concentration at the inlet was used as a nondimensional standard, denoted as C inlet = 1. Initially there is no particle in the domain, i.e. C t = 0 = 0. The particles were set to attach to walls upon contact and can leave the domain from the outlet. The above parameters were set to be consistent with the validation experiment.
The computational domain was then discretised into a hexahedral

Table 1
The details of virus import due to coughing and speaking (Chao et al., 2009 mesh, as shown in Fig. 2(b). A mesh sensitivity test is presented with three different cell sizes, respectively 0.05 m (coarse), 0.04 m (fine) and 0.03 m (very fine). The three mesh sizes were tested with a maximum Courant number of 1 to determine the corresponding timestep size. Simulations using the three sets of meshes were run for 60 s, and the same measurements as per the experiment were taken for comparison, i. e. the velocity profile and particle distribution were measured across the centre plane of the box. To assess the numerical uncertainty from spatial discretisation, an estimation was conducted as reported in Appendix A. The Grid Convergence Index (GCI) method (Celik et al., 2008) was used and the numerical uncertainty in the fine-grid solution for the fine mesh turned out to be 3.68%. Figs. 3 and 4 show a qualitative comparison between the experimental measurements and simulations performed with the three mesh densities. Overall there is good consistency between the experiment, CFD with fine mesh, and CFD with very fine mesh. This can be seen in both the velocity and concentration results. However, there are certain inaccuracies in the coarse mesh results, as circled in the figures. Therefore, the fine mesh density was chosen for the following investigations, as it requires less computational recourses than the very fine mesh whilst maintaining the required accuracy.
Furthermore, a quantitive comparison was performed between the experiment and CFD with fine mesh. Specific velocity data measured in the experiment are compared with corresponding CFD results, as plotted in Fig. 5. Good agreement can be seen for all the data points, which confirms the accuracy of the CFD model. Based on the results presented in this section, the present computational approach is deemed suitable to study the airborne transmission of COVID-19 virus.

Ship model and COVID-19 risks
Upon validation of the computational approach, a small passenger ship operating in Indonesia was selected as the research object of this paper. The vessel's photo and geometry drawings are shown in Figs. 6  (1) The operation of this vessel type in Indonesia has been significantly impacted ships by COVID-19. The country, heavily reliant  on sea transportation, is looking to recover its crew and passenger operations to aid the economic situation. (2) The ship's superstructure is compact, and the average voyage time is 12 h, which gives a high-risky environment of COVID-19 transmission where people stay in a crowded space for a fairly long time.
There are two types of virus import mechanisms considered in this work: a passenger coughing and speaking. Both are the most possible initiations of how COVID-19 starts to transmit in such a ship. The virus particle details of coughing and speaking used in this work were set according to the measurements of Chao et al. (2009), as given in Table 1. Coughing is a short event whose duration is considered to be 0.3 s, and speaking is modelled to last 60 s. The viruses injected through coughing have a higher concentration and initial speed than those from speaking, while overall speaking produces more floating viruses as its duration is much longer.
As long as viruses are imported, their transmission relies on airflows. There can be two typical types of airflow in the present case: (a) external airflow comes from the vessel's forward door; (b) internal airflow from ACs. For modelling both the external and internal airflows, the vessel's superstructure was imported into the CFD software at full scale, establishing a computational domain as shown in Fig. 8. The domain was discretised using the fine mesh density as per the reported mesh sensitivity test. CFD investigations were then performed using the approach introduced in Section 2. The COVID-19 transmission due to the two types of airflows was analysed respectively in Sections 4 and 5.

External airflow entering the vessel
To study the impact of external airflow entering the vessel on the COVID-19 transmission, the vessel was assumed to advance at a constant speed (V). Four case studies were conducted for V = 6 knots, as a combination of the situations when a passenger sitting in the first row is  When the forward door is open, the forward door was set as "fixed-velocity inlet" with a constant velocity of (-V, 0, 0), and the back door was set as "fixed-pressure outlet". Other boundaries were set as "non-slip walls". When the forward door is closed, all boundaries were set as "nonslip walls" and there is no wind flow in the domain.
For the open-door cases, a significant airflow forms inside the vessel. As shown in Fig. 9, this flow takes around 5 s of simulation to converge, thus each of the following simulations was first run for 10 s without particles to ensure the flow convergence. After 10 s, virus particles were injected, assuming from an infected passenger sitting in the first row.
For the simulation of a passenger coughing with the forward door open, it can be seen in Fig. 10 that viruses were coughed out and scattered. Along with the airflow, the viruses moved rapidly towards the back door. For around 5 s, the passengers behind the coughing person were extensively contacted by the viruses, after which the viruses were mostly blown out from the vessel.
For the simulation of a passenger coughing with the forward door closed, it can be seen in Fig. 11 that viruses were coughed out and then only stayed in the area where the passenger sits. The virus movement was mainly a slow sinking due to gravity, alongside a small diffusion due to stochastic motions. Although the viruses stayed in the air for around 100 s, the contagion risk appears to be minimal, based on the assumption that coughing is usually not made directly towards other people.
For the simulation of a passenger speaking with the forward door open, it can be seen in Fig. 12 that a wake of viruses was created and severely affected the passengers behind the speaking person, especially the next two rows. When the speaking stopped, the viruses were carried away from the ship in 10 s.
For the simulation of a passenger speaking with the forward door closed, it can be seen in Fig. 13 that a significant number of viruses were outputted and remained in a small area in front of the speaking person. However, since speaking usually occurs as one person facing another, a   contagion risk exists if the conversating people are sufficiently close to each other. It is suggested that a safe distance should be half a metre, according to the virus coverage shown in Fig. 13(a). This confirms that it is necessary to keep social distancing in the installed seats.
Combining the results from the four cases, it is shown that: when the ship's forward door is open, a significant airflow forms in the ship, which carries the viruses to make extensive contacts with the passengers in the back seat rows; when the forward door is closed, the viruses mainly sink due to gravity and the diffusion is limited to a small area.
These two behaviours are also observed by relevant experimental and computational COVID-19 studies for other environments, as summarised in the review of Katre et al. (2021). More ship speed conditions (V = 12 and 18 knots) have also been tested for the open-door scenario, concerning an infected passenger speaking. It is found that the virus distribution is similar to that of V = 6 knots, despite that the virus spread is smaller when V is higher, as shown in Fig. 14. Overall, it is recommended to keep the forward door closed to minimise the virus's diffusion, although this might be counter-intuitive. It is also found that speaking generally creates a higher risk than coughing, as speaking usually lasts a much longer duration, thereby more viruses are introduced to the air. Whilst speaking may have been less altered than coughing which is more likely to be treated as a red flag, the present research suggests that more attention should be paid to the COVID-19 risk in daily conversations.
When there is no external airflow, the modelling indicated that a conversation between two people should keep a distance of at least half a metre (less than a seat's width). Based on this, Fig. 15 presents two potential seat arrangements for the ship. The aligned arrangement shown in Fig. 15(a) reduces the capacity by 33%, and the crossed arrangement shown in Fig. 15(b) reduces the capacity by 50%. However, as the setting in Fig. 15(a) may not avoid the risk from a front passenger who turns around and speaks with the passenger behind, the social distancing setting in Fig. 15(b) is recommended.

Internal air conditioner flow
There are two wall-mounted ACs installed inside the ship, respectively in the front and back as shown in Fig. 16 (AC1 and AC2). Each AC has a size of approximately 0.25 m × 1.1 m × 0.45 m, but it is not cubic, as shown in Fig. 17. The AC has an air outlet near the bottom and a return air inlet at the top. The air outlet area is 1.1 m × 0.05 m, and the return air inlet is 0.7 m × 0.25 m. In the CFD model, the AC's outlet was set as "fixed-velocity inlet" with a constant speed of 2 m/s, which was measured on-site when the AC was operating at its middle power. The return air inlet was set as "fixed-velocity outlet" with a constant speed of 0.63 m/s, which was calculated based on volume conservation, i.e. the air amount that exits from the air outlet equals that enters the return air inlet (2 m/s × 1.1 m × 0.05 m ≈ 0.63 m/s × 0.7 m × 0.25).
This study investigates the influence of each AC's airflow direction on the transmission of COVID-19. The airflow direction from the air outlet was varied between 0 • and 60 • (relative to horizontal, θ), with four cases studied respectively for AC1 and AC2, where θ = 0 • , 15 • , 30 • and 60 • . The virus source is assumed as an infected passenger sitting on a seat nearby the opening AC (as marked in Fig. 16), and the person is considered to speak for 60 s.
Figs. 18 and 19 show the velocity field and virus distribution inside the ship, when AC1 or AC2 is operating. It is found that a wall-mounted AC can generate a flow circle that is highly dependent on θ. When θ is 0 • or 15 • , the AC flow was confined in the top part of the room and within a relatively small region, so did the virus transmission. When θ is 30 • or 60 • , the virus spread was evidently expanded by the AC flow, which is particularly true for AC2, as shown in Fig. 19(c)&(d). It is also found that an AC tends to accumulate the virus particles, as in both Figs. 18 and 19 where the virus particles gathered near the opening AC. This is because an AC's backflow attracts virus particles to move toward the device.
Based on the findings above, two suggestions are given for the AC operation on such a passenger vessel: (a) control the AC outlet direction at less than 15 • downward, and (b) arrange passengers to not sit nearby an operating AC. The second suggestion can be adapted to other AC types whose inlet and outlet are at separate locations in a room (such as the setup in Fig. 1), and the suggestion is to not sit downstream of the AC flow.

Conclusions
To provide effective measures that can minimise COVID-19 transmission for passenger vessels, a computational model has been established to investigate the airborne transmission of the virus in the superstructure of a small passenger vessel. The model was validated against experimental results to prove the capability of accurately predicting the velocity field and virus distribution inside a room. Based on the validated model, a series of simulations were conducted to study the influence on the virus transmission from both external wind flow and internal AC flow. The simulation results have helped identify operational improvements as summarised below.
When the forward door is open, ship advancement generates an extensive wind flow across the passenger area, which fosters the spread of virus. Therefore, it is suggested to keep the ship's forward door shut. When there is no wind flow in the vessel's superstructure, the virus spread from coughing or speaking is limited to a radius of half a metre. Based on the radius, a crossed seat arrangement plan has been proposed in the present paper.
Although wall-mounted ACs could also foster the spread of virus in a vessel, this study has demonstrated that this effect can be suppressed by controlling the AC outlet direction to be less than 15 • downward. In addition, it is found that virus particles can follow an AC's backflow to accumulate. Hence, sitting far from an opening wall-mounted AC can minimise the associated risk.
In future work, the computational approach can be applied to study the COVID-19 airborne transmission in other environments. Many maritime environments are still at COVID-19 risk which requires more research, such as a large cruise ship, an open-air finishing vessel and an offshore platform.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Step 4 : Calculated the extrapolated value: Step 5 : Calculated the approximate relative error: Calculated extrapolated relative error: Calculated the fine-grid convergence index: GCI 21 fine = 1.25e 21 a r P 21 − 1 The results are summarised in Table A1, in which the numerical uncertainty in the fine-mesh solution for the velocity magnitude is 3.68%